Battery-free implantable sensor

1. CS39NThe Beauty and Joy of ComputingLecture #11Recursion III 2009-11-09 UC BerkeleyComputer ScienceLecturer SOEDan Garcia It has been a challenge to power electronic components implanted within a body. Researchers at UW have developed a new chip that needs less power, and can be powered from outside the body (1 meter away) Battery-free implantable sensor technologyreview.com/computing/23878

2. Lecture Overview • Local vs Global drawing • Example: Twig • Example: C-Curve • Lindenmayer (L) systems • Fibonacci & the golden mean • Panspermia • Summary Great reference text!

3. Local vs Global Drawing (394,27)pointing 48º • Local (turtle) Drawing • Concept of pen, sprite facing some direction • State! (where sprite ends) • Specify via local coords • Example • Move turtle to (394,27) • Face 48º • Pen down • Move 100 • Pen up • Move -50 • Turn right 90º • Move -50 • Pen down • Move 100 • Global (god) Drawing • No pen, just geometric primitives (DrawLine etc) • Stateless • Specify via global coords • Example • SW corner = (394,27) • Calculate NE corner • How? Simple trig, function of (394,27), 100, 48º • DrawLine (SW,NE) • Calculate NW corner • Calculate SE corner • DrawLine (NW,SE) Goal: Draw a 100-length “+” from point (394,27) at 48º “Turtle” Graphics invented byPapert Scratch  Where sprite ends matters!

4. Example: Twig • Want to draw a twig • Where does sprite end? • Could add randomness • Lots of variations • # branches • Angle Two copies of last recursion level rotated 20º Notice drawing happens at every level … n=0 n=1 n=2 …

5. Example: C-curve, Dragon curve • C-curve • break a straight line up to form 90º angle • Left out, Right out • Dragon curve • break a straight line up to form 90º angle • Left out, Right in … … n=0 n=1 n=2 n=0 n=1 n=2 … … Notice drawing only happens in base case Notice drawing only happens in base case

6. Example: Peano Curve • Simple rewrite rule • Replace every straight line w/9 smaller lines, each a third the size(like an 8 with side lines) • As n∞, notice… • Space-filling! • Converging shape? Notice drawing only happens in base case … … n=0 n=1 n=2

7. en.wikipedia.org/wiki/L-system Lindenmayer (L) systems • Rewriting system for • Modeling plant growth • Generating fractals, languages, … • Basics • Variables (replaced each level) • Constants (not replaced) • Start (i.e., base case) • Rewrite rules (Recursive case) •  Example: Fibonacci • Variables: A B • Start: A • Rules: (A  B, B  AB) • Example: Dragon Curve • Variables : X Y • Constants : F + − • Start: FX • Rules (angle : 90°) • (X → X+YF) • (Y → FX-Y) • F means "draw forward" • - means "turn left 90°" • + means "turn right 90°". • X and Y do not correspond to any drawing action and are only used to control the evolution of the curve Leonardo de Pisaaka, Fibonacci n = 0 : A (1) n = 1 : B (1) n = 2 : AB (2) n = 3 : BAB (3) n = 4 : ABBAB (5) n = 5 : BABABBAB (8) n = 6 : ABBABBABABBAB (13) n = 7 : BABABBABABBABBABABBAB (21)

8. en.wikipedia.org/wiki/L-system Panspermia • panspermia |panˈspərmēə| • the theory that life on the earth originated from microorganisms or chemical precursors of life present in outer space and able to initiate life on reaching a suitable environment • Also, 1990 film by Karl Sims (famous computer graphics research and artist) • “Attempts were made to bring together several concepts: chaos, complexity, evolution, self propagating entities, and the nature of life itself.” Scenes from Panspermia L-systems plant growth

9. Summary • Fractals can model coastlines, clouds, plants, trees, natural growth • Fibonacci 1st to see this • When authoring fractals, make sure you’re clear when pen goes up/down and where begins/ends • Scratch has Turtle graphics • Infinite recursion = fun